Question

A couple took out a 5-year $30,000 loan to pay for for their wedding. After 5 years, the loan payments they had made to the bank amounted to $38,250.

The interest rate on the loan, compounded continuously, is %. If they had taken an 8-year loan instead of a 5-year loan, they would have paid approximately $ more.

Answer 1

the formula for continuous interest is A = P*e^(r*t) where A is the amount paid, P is the amount taken out for a loan, r is the interest rate, t is the number of years, e is a mathematical constant

so you would first plug in 38,250 for the amount paid A
30,000 for the amount taken out, P
5 for the number of years

to calculate the interest rate

then you would go back and plug in t = 8 to figure out the amount paid for the 8-year loan

then you'd subtract amt. paid for 8 year loan, minus amt. paid for 5 year loan

Answer 2

still there? I am happy to help with the calculations if something is still unclear

Answer 3

its very unclear

Answer 4

alright, let's start with the first step.

A = P*e^(rt)

as I said before, A is the amount paid, so A = 38,250
P is the amount taken out for a loan, so P = 30,000
the loan period is 5 years to t = 5

plugging everything in:

38250 = 30000*e^(r*5)

solve for r

Answer 5

how do you solve for r?

Answer 6

remember your rules for isolating a variable

we want "r" by itself

38250 = 30000*e^(r*5)

notice how the right side is being multiplied by 30,000. we do the opposite, so we divide both sides by 30,000 to isolate r

(38250/30000) = e^(r*5)

now, we have e raised to the 5r power. to undo the e, we take the natural log of both sides

ln(38250/30000) = 5r

now, since r is being multiplied by 5, we "undo" this by dividing both sides by r.

r = ln(38250/30000) / 5 = ?

Answer 7

thank you I got my answer